This invention relates to a method of measuring the mass flow rate of a gaseous or vaporous fluid on the Coriolis principle.
This is accomplished by means of Coriolis mass flow/density meters, which, as is well known, have at least one bent or straight flow tube that is vibrated while a fluid flows through it.
Usually, at least one vibrator and at least two vibration sensors are mounted on the flow tube, the vibration sensors being positioned at a given distance from each other in the direction of flow. The flow tube generally vibrates at a mechanical resonance frequency that is predetermined by its material and dimensions but is varied by the density of the fluid. In other cases, the vibration frequency of the flow tube is not exactly the mechanical resonance frequency of the flow tube, but a frequency in the vicinity thereof.
The vibration sensors deliver analog signals whose frequency is equal to the vibration frequency of the flow tube, and which are separated in time, i.e., between which a phase difference exists when the fluid flows through the flow tube. From this phase difference, a signal representing a time difference, e.g. between zero crossings of the sensor signals, can be derived which is directly proportional to mass flow rate, as is described, for example, in U.S. Pat. No. 4,187,721.
It is also possible, however, to derive from the phase difference an angle difference which, after being divided by 2xcfx80 times the resonance frequency f of the flow tube, is directly proportional to mass flow rate, as is described in U.S. Pat. No. 5,648,616 or EP-A 866 319.
In the measurement of the mass flow rate of liquids, the aforementioned proportionalities can always be assumed to be exact, so that with present-day Coriolis mass flow/density meters, a measurement accuracy of 0.1% can be guaranteed.
As the inventors have found, this exact proportionality cannot be assumed in most measurements of gaseous or vaporous fluids, which results in reduced accuracy.
It is therefore an object of the invention to provide a method of measuring the mass flow rate of a gaseous or vaporous fluid on the Coriolis principle whose accuracy is comparable to that of the measurement of liquids.
To attain this object, the invention provides a method of measuring the mass flow rate of a gaseous or vaporous fluid flowing through at least one flow tube of a mass flow sensor of a Coriolis mass flow/density meter, which flow tube
vibrates in operation at a frequency f predetermined by its material and dimensions but varied by the density of the fluid, said frequency being equal to or in the vicinity of the instantaneous mechanical resonance frequency of the flow tube,
has attached to it a first vibration sensor,
which delivers a first sensor signal, and
a second vibration sensor,
which delivers a second sensor signal,
the first and second vibration sensors being positioned at a given distance from each other in the direction of flow, and
a vibrator, and
is surrounded by a support frame or a support tube or held by a support plate so as to be capable of vibrating,
said method comprising the steps of forming from the first and second sensor signals a signal dependent on a phase difference between the sensor signals, and multiplying said signal by a function f(c) dependent on the speed of sound c in the fluid.
In a first embodiment of the invention, the signal dependent on the phase difference represents a time difference between zero crossings of the sensor signals.
In a second embodiment of the invention, the signal dependent on the phase difference represents an angle difference, and the latter is divided by 2xcfx80 times the vibration frequency f.
In a third embodiment of the invention, which is also applicable to the first or second embodiment, the function f(c) has the form
f(c)={1+bxc2x7(2xcfx80xc2x7fxc2x7d/c)2}xe2x88x921
where
b is a constant determined by calibration and identical for all nominal diameters of the flow tube, and
d is its internal diameter.
In a further embodiment of the invention, the speed of sound c is approximated by a function f(Tm) dependent on the current temperature Tm of the flow tube, particularly by a function of the form: c=c0+c1xc2x7Tm, where c0, c1 are fluid-specific constants.
One advantage of the invention is that the speed of sound in the fluid, and thus indirectly the compressibility of the fluid, can be taken into account in the measurement, so that the accuracy of the mass flow measurement of gaseous or vaporous fluids can be made virtually identical to that of the measurement of liquids.